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首页> 外文期刊>The Review of Economic Studies >Approximate Permutation Tests and Induced Order Statistics in the Regression Discontinuity Design
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Approximate Permutation Tests and Induced Order Statistics in the Regression Discontinuity Design

机译：回归不连续设计中的近似排列测试和诱导顺序统计

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摘要

In the regression discontinuity design (RDD), it is common practice to assess the credibility of the design by testing whether the means of baseline covariates do not change at the cut-off (or threshold) of the running variable. This practice is partly motivated by the stronger implication derived by Lee (2008), who showed that under certain conditions the distribution of baseline covariates in the RDD must be continuous at the cut-off. We propose a permutation test based on the so-called induced ordered statistics for the null hypothesis of continuity of the distribution of baseline covariates at the cut-off; and introduce a novel asymptotic framework to analyse its properties. The asymptotic framework is intended to approximate a small sample phenomenon: even though the total number n of observations may be large, the number of effective observations local to the cut-off is often small. Thus, while traditional asymptotics in RDD require a growing number of observations local to the cut-off as n - 8, our framework keeps the number q of observations local to the cut-off fixed as n - 8. The new test is easy to implement, asymptotically valid under weak conditions, exhibits finite sample validity under stronger conditions than those needed for its asymptotic validity, and has favourable power properties relative to tests based on means. In a simulation study, we find that the new test controls size remarkably well across designs. We then use our test to evaluate the plausibility of the design in Lee (2008), a well-known application of the RDD to study incumbency advantage.
机译：在回归不连续设计（RDD）中，通常的做法是通过测试基线协变量的平均值是否在运行变量的截止点（或阈值）发生变化来评估设计的可信度。这种做法的部分动机是Lee（2008）得出的更强烈的含义，他表明在某些条件下，RDD中基线协变量的分布必须在截止点处是连续的。我们提出了一种基于所谓诱导有序统计的置换检验，用于在截止点处基线协变量分布连续性的零假设；并引入一个新的渐近框架来分析其性质。渐近框架旨在近似一个小样本现象：尽管观测总数n可能很大，但截止点附近的有效观测数通常很小。因此，虽然RDD中的传统渐近性需要越来越多的观测值，但在截止点附近，如n-；8.我们的框架将局部观测值的数量q固定为n-；8.新测试易于实现，在弱条件下渐近有效，在比其渐近有效性所需的条件更强的条件下表现出有限样本有效性，并且相对于基于均值的测试具有良好的幂性质。在一项模拟研究中，我们发现新的测试可以很好地控制各种设计的尺寸。然后，我们使用我们的测试来评估Lee（2008）中设计的合理性，Lee（2008）是RDD研究在职优势的著名应用。

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